# Calculus problem

1. Nov 6, 2008

### farmd684

1. The problem statement, all variables and given/known data
show f(x)=x^3-3x^2+2x is not one to one on (-infinity,+infinity)

2. Relevant equations

finding the largest value of k such as f is one to one on interval (-k,k)
3. The attempt at a solution
i can get f`(x)=3x^2-6x+2 but it is positive so f(x) should be one-to-one
how to prove it

2. Nov 6, 2008

### Dick

f(x)=3x^2-6x+2 isn't positive. f(1)=-1.

Last edited by a moderator: Nov 7, 2008
3. Nov 7, 2008

### HallsofIvy

Staff Emeritus
I just automatically looked at the discrimant for 3x2- 6x+ 2:
$$\sqrt{6^2- 4(3)(2)}= \sqrt{36- 24}= \sqrt{12}$$
Since that is a real number, the 3x2- 6x+2 changes sign, and the original function changes "direction", at two places.

4. Nov 7, 2008

### farmd684

thanks but how can i do this
largest value of k such as f is one to one on interval (-k,k)

5. Nov 7, 2008

### HallsofIvy

Staff Emeritus
A function f(x) is one-to-one as long as its derivative does not change sign- and a continuous derivative, such as the derivative of any polynomial, can change sign only where the derivative is 0.

Solve 3x2- 6x+ 2= 0, say by using the quadratic formula. Those 2 values will give 3 intervals on which the function is one to one. One of them contains the an interval of the form (-k, k).